Numerical Methods for Simultaneous Diagonalization

Numerical Methods for Simultaneous Diagonalization (1993)

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by Angelika Bunse-Gerstner , Ralph Byers , Volker Mehrmann

Venue:	SIAM J. Matrix Anal. Applicat
Citations:	28 - 0 self

BibTeX

@ARTICLE{Bunse-Gerstner93numericalmethods,
    author = {Angelika Bunse-Gerstner and Ralph Byers and Volker Mehrmann},
    title = {Numerical Methods for Simultaneous Diagonalization},
    journal = {SIAM J. Matrix Anal. Applicat},
    year = {1993},
    volume = {14},
    pages = {927--949}
}

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Abstract

We present a Jacobi-like algorithm for simultaneous diagonalization of commuting pairs of complex normal matrices by unitary similarity transformations. The algorithm uses a sequence of similarity transformations by elementary complex rotations to drive the off-diagonal entries to zero. We show that its asymptotic convergence rate is quadratic and that it is numerically stable. It preserves the special structure of real matrices, quaternion matrices and real symmetric matrices.

Citations

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